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Supported only in the two 1905 Einstein's papers on Relativity and a very rigid respect for the historical context, an analysis is done of the derivation of the universal mass-energy relationship. It is found, contrary to the today accepted…

The Einstein equivalence principle is based on the equality of gravitational mass and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a…

A historical experiment by K\"undig on the transverse Doppler shift in a rotating system measured with the M\"ossbauer effect has been recently first re-analyzed and then replied [1,2]. The results have shown that a correct re-processing of…

While it is widely believed that gravity should ultimately be treated as a quantum theory, there remains a possibility that general relativity should not be quantized. If this is the case, the coupling of classical gravity to the…

Einstein's happiest thought was his leap from the observation that a falling person feels no gravity to the realization that gravity might be equivalent to acceleration. It affects all bodies in the same way because it is a property of…

The extreme smallness of both the Planck length, on the one side, and the ratio of the gravitational to the electrical forces between, say, two electrons, on the other side has led to a widespread belief that the realm of quantum gravity is…

Evolution of gravitational perturbations, both in time and frequency domains, is considered for a spherically symmetric black hole in the non-reduced Einstein-Aether theory. It is shown that real oscillation frequency and damping rate are…

Combining gravity with quantum mechanics remains one of the biggest challenges of physics. In the past years, experiments with opto-mechanical systems have been proposed that may give indirect clues about the quantum nature of gravity. In a…

Atomic clocks have recently reached a fractional timing precision of $<10^{-18}$. We point out that an array of atomic clocks, distributed along the Earth's orbit around the Sun, will have the sensitivity needed to detect the time dilation…

The Equivalence Principle (EP) is at the heart of General Relativity (GR), tested in many aspects. It is often used to discuss qualitatively the influence of gravity on physical phenomena. But can this be made more precise? We compare clock…

Clocks play a special role at the interface of general relativity and quantum mechanics. We analyze a clock-interferometry thought experiment and go on to theoretically derive and experimentally test a complementarity relation for quantum…

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are…

In special and general relativity the synchronization convention of distant clocks may be simulated with a mathematical definition of global non-inertial frames (the only ones existing in general relativity due to the equivalence principle)…

The properties of light in the presence of electromagnetic and gravitational fields are compared. Once one takes account of the fact that clock rates vary with distance from a massive object, it is argued that in an absolute sense light…

The interplay of gravitation and the quantum-mechanical principle of linear superposition induces a new set of neutrino oscillation phases. These ensure that the flavor-oscillation clocks, inherent in the phenomenon of neutrino…

A quantum measurement-like event can produce any of a number of macroscopically distinct results, with corresponding macroscopically distinct gravitational fields, from the same initial state. Hence the probabilistically evolving…

The Atomic Clock Ensemble in Space (ACES) mission is developing high performance clocks and links for space to test Einstein's theory of general relativity. From the International Space Station, the ACES payload will distribute a clock…

Contrary to general belief, the Fraunhofer lines have been found to be plasma redshifted and not gravitationally redshifted, when observed on Earth. Quantum mechanical effects cause the photons' gravitational redshift to be reversed as the…

The confrontation between Einstein's gravitation theory and experimental results, notably binary pulsar data, is summarized and its significance discussed. Experiment and theory agree at the 10^{-3} level. All the basic structures of…

Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and…